If he had it in writing, this wouldn't be a lawsuit. Zenimax wouldn't make the very specific claims that they've made now, unless they felt like they had pretty rock solid evidence. When you're dealing with a more "he said, she said" legal tiff, the plaintiffs usually use language that gives the defendant an out. "We believe" or "It appears" or "we suspect" and "may" would show up in the accusations. That way, the defendant has an easier time publicity-wise saying "Whoops, someone goofed. Here's some money."
In this case, Zenimax is being very, very specific and has been from the start. They say Carmack took files from Zenimax owned systems and that is the *biggest* no-no in the book. It's entirely likely that Zenimax knew he was collaborating with Oculus and was fine with it, but that they didn't want anything Carmack did while working for them to *officially* become Oculus IP. And then, Carmack not only leaves, but if he took things *with* him, that's a pretty severe case of IP theft. Even if none of that code actually got directly used in Oculus products, if it was used as a basis for any component required by Oculus that Carmack had a hand in generating while he was at Zenimax, he's fucked himself.
The only way for Carmack to have done things cleanly was to have absolutely no possible hint that he would have done what Zenimax is claiming he did so he could claim that he used knowledge in his head but *not* anything produced while working for Zenimax beyond that. And if Zenimax is telling the truth, he fucked up that *one* job.